__________________"I refuse to prove that I exist," says God, "for proof denies faith, and without faith I am nothing." "But," says Man, "The Babel fish proves you exist, and so therefore, by your own arguments, you don't." "Oh dear," says God, "I hadn't thought of that," and promptly vanished in a puff of logic.

I don't know if its a common problem per se but there are diseases which are thought to be induced by the psychologist through basically the power of suggestion/being in a distressed state. Multiple personalities is I think an example of this from what i remember.

there's like an article on wikipedia about iatrogenic mental illnesses: